{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Model comparison\n",
    "\n",
    "To demonstrate the use of model comparison criteria in PyMC3, we implement the **8 schools** example from Section 5.5 of Gelman et al (2003), which attempts to infer the effects of coaching on SAT scores of students from 8 schools. Below, we fit a **pooled model**, which assumes a single fixed effect across all schools, and a **hierarchical model** that allows for a random effect that partially pools the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import pymc3 as pm\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-darkgrid')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The data include the observed treatment effects and associated standard deviations in the 8 schools."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "J = 8\n",
    "y = np.array([28,  8, -3,  7, -1,  1, 18, 12])\n",
    "sigma = np.array([15, 10, 16, 11,  9, 11, 10, 18])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Pooled model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [mu]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:01<00:00, 1622.25draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as pooled:\n",
    "    mu = pm.Normal('mu', 0, sigma=1e6)\n",
    "    \n",
    "    obs = pm.Normal('obs', mu, sigma=sigma, observed=y)\n",
    "    \n",
    "    trace_p = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace_p);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Hierarchical model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [tau, mu, eta]\n",
      "Sampling 2 chains: 100%|██████████| 3000/3000 [00:02<00:00, 1359.34draws/s]\n",
      "There were 4 divergences after tuning. Increase `target_accept` or reparameterize.\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as hierarchical:\n",
    "    \n",
    "    eta = pm.Normal('eta', 0, 1, shape=J)\n",
    "    mu = pm.Normal('mu', 0, sigma=1e6)\n",
    "    tau = pm.HalfCauchy('tau', 5)\n",
    "    \n",
    "    theta = pm.Deterministic('theta', mu + tau*eta)\n",
    "    \n",
    "    obs = pm.Normal('obs', theta, sigma=sigma, observed=y)\n",
    "    \n",
    "    trace_h = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/junpenglao/Documents/pymc3/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x144 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace_h, varnames=['mu']);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/home/junpenglao/Documents/pymc3/pymc3/plots/__init__.py:40: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x403.2 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.forestplot(trace_h, varnames=['theta']);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Widely-applicable Information Criterion (WAIC)\n",
    "\n",
    "WAIC (Watanabe 2010) is a fully Bayesian criterion for estimating out-of-sample expectation, using the computed log pointwise posterior predictive density (LPPD) and correcting for the effective number of parameters to adjust for overfitting."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61.173190685882204"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pooled_waic = pm.waic(trace_p, pooled)\n",
    "    \n",
    "pooled_waic.WAIC"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61.38571263305805"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hierarchical_waic = pm.waic(trace_h, hierarchical)\n",
    "    \n",
    "hierarchical_waic.WAIC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "PyMC3 includes two convenience functions to help compare WAIC for different models. The first of this functions is `compare`, this one computes WAIC (or LOO) from a set of traces and models and returns a DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "hierarchical.name = 'hierarchical'\n",
    "pooled.name = 'pooled'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "      <th>dSE</th>\n",
       "      <th>var_warn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pooled</th>\n",
       "      <td>61.17</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2.2</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hierarchical</th>\n",
       "      <td>61.39</td>\n",
       "      <td>0.99</td>\n",
       "      <td>0.21</td>\n",
       "      <td>0</td>\n",
       "      <td>2.01</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               WAIC pWAIC dWAIC weight    SE   dSE var_warn\n",
       "pooled        61.17  0.69     0      1   2.2     0        0\n",
       "hierarchical  61.39  0.99  0.21      0  2.01  0.31        0"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_comp_WAIC = pm.compare({hierarchical: trace_h, pooled: trace_p})\n",
    "df_comp_WAIC"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We have many columns so let check one by one the meaning of them:\n",
    "\n",
    "\n",
    "1. The first column clearly contains the values of WAIC. The DataFrame is always sorted from lowest to highest WAIC. The index reflects the order in which the models are passed to this function.\n",
    "\n",
    "2. The second column is the estimated effective number of parameters. In general, models with more parameters will be more flexible to fit data and at the same time could also lead to overfitting. Thus we can interpret pWAIC as a penalization term, intuitively we can also interpret it as measure of how flexible each model is in fitting the data. \n",
    "\n",
    "3. The third column is the relative difference between the value of WAIC for the top-ranked model and the value of WAIC for each model. For this reason we will always get a value of 0 for the first model.\n",
    "\n",
    "4. Sometimes when comparing models, we do not want to select the \"best\" model, instead we want to perform predictions by averaging along all the models (or at least several models). Ideally we would like to perform a weighted average, giving more weight to the model that seems to explain/predict the data better. There are many approaches to perform this task, one of them is to use Akaike weights based on the values of WAIC for each model. These weights can be loosely interpreted as the probability of each model (among the compared models) given the data. One caveat of this approach is that the weights are based on point estimates of WAIC (i.e. the uncertainty is ignored).\n",
    "\n",
    "5. The fifth column records the standard error for the WAIC computations. The standard error can be useful to assess the uncertainty of the WAIC estimates. Nevertheless, caution need to be taken because the estimation of the standard error assumes normality and hence could be problematic when the sample size is low.\n",
    "\n",
    "6. In the same way that we can compute the standard error for each value of WAIC, we can compute the standard error of the differences between two values of WAIC. Notice that both quantities are not necessarily the same, the reason is that the uncertainty about WAIC is correlated between models. This quantity is always 0 for the top-ranked model.\n",
    "\n",
    "7. Finally we have the last column named \"warning\". A value of 1 indicates that the computation of WAIC may not be reliable, this warning is based on an empirical determined cutoff value and need to be interpreted with caution. For more details you can read this [paper](https://arxiv.org/abs/1507.04544)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The second convenience function takes the output of `compare` and produces a summary plot in the style of the one used in the book [Statistical Rethinking](http://xcelab.net/rm/statistical-rethinking/) by Richard McElreath (check also [this port](https://github.com/aloctavodia/Statistical-Rethinking-with-Python-and-PyMC3) of the examples in the book to PyMC3)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.compareplot(df_comp_WAIC);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The empty circle represents the values of WAIC and the black error bars associated with them are the values of the standard deviation of WAIC. \n",
    "\n",
    "The value of the lowest WAIC is also indicated with a vertical dashed grey line to ease comparison with other WAIC values.\n",
    "\n",
    "The filled black dots are the in-sample deviance of each model, which for WAIC is  2 pWAIC from the corresponding WAIC value.\n",
    "\n",
    "For all models except the top-ranked one we also get a triangle indicating the value of the difference of WAIC between that model and the top model and a grey errobar indicating the standard error of the differences between the top-ranked WAIC and WAIC for each model."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Leave-one-out Cross-validation (LOO)\n",
    "\n",
    "LOO cross-validation is an estimate of the out-of-sample predictive fit. In cross-validation, the data are repeatedly partitioned into training and holdout sets, iteratively fitting the model with the former and evaluating the fit with the holdout data. Vehtari et al. (2016) introduced an efficient computation of LOO from MCMC samples, which are corrected using Pareto-smoothed importance sampling (PSIS) to provide an estimate of point-wise out-of-sample prediction accuracy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61.203032352985645"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pooled_loo = pm.loo(trace_p, pooled)\n",
    "    \n",
    "pooled_loo.LOO"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "61.47557753820364"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "hierarchical_loo  = pm.loo(trace_h, hierarchical)\n",
    "    \n",
    "hierarchical_loo.LOO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can also use `compare` with LOO."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>LOO</th>\n",
       "      <th>pLOO</th>\n",
       "      <th>dLOO</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "      <th>dSE</th>\n",
       "      <th>shape_warn</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>pooled</th>\n",
       "      <td>61.2</td>\n",
       "      <td>0.7</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>2.21</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>hierarchical</th>\n",
       "      <td>61.48</td>\n",
       "      <td>1.03</td>\n",
       "      <td>0.27</td>\n",
       "      <td>0</td>\n",
       "      <td>2.01</td>\n",
       "      <td>0.31</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                LOO  pLOO  dLOO weight    SE   dSE shape_warn\n",
       "pooled         61.2   0.7     0      1  2.21     0          0\n",
       "hierarchical  61.48  1.03  0.27      0  2.01  0.31          0"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_comp_LOO = pm.compare({hierarchical: trace_h, pooled: trace_p}, ic='LOO')\n",
    "df_comp_LOO"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The columns return the equivalent values for LOO, notice that in this example we get two warnings. Also notice that the order of the models is not the same as the one for WAIC.\n",
    "\n",
    "We can also plot the results"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x144 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.compareplot(df_comp_LOO);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Interpretation\n",
    "\n",
    "Though we might expect the hierarchical model to outperform a complete pooling model, there is little to choose between the models in this case, giving that both models gives very similar values of the information criteria. This is more clearly appreciated when we take into account the uncertainty (in terms of standard errors) of WAIC and LOO.\n",
    "\n",
    "## Reference\n",
    "\n",
    "[Gelman, A., Hwang, J., & Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24(6), 997–1016.](https://doi.org/10.1007/s11222-013-9416-2)\n",
    "\n",
    "[Vehtari, A, Gelman, A, Gabry, J. (2016). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing](http://link.springer.com/article/10.1007/s11222-016-9696-4)"
   ]
  }
 ],
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   "display_name": "Python 3",
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    "version": 3
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   "file_extension": ".py",
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   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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